$$\lambda = \frac{h}{mv}$$
where:
- λ is the de Broglie wavelength in meters (m)
- h is the Planck constant ( 6.626 x 10-34 Js)
- m is the mass of the object in kilograms (kg)
- v is the velocity of the object in meters per second (m/s)
First, convert the mass to kilograms:
$$m = 12.4g (\frac{1 kg}{1000g})= 0.0124 kg$$
Then, convert the velocity to meters per second:
$$v = (1.2 \times 10^2 mph) (\frac{1609.344 m}{1 mi})(\frac{1 h}{3600 s}) = 53.6448 m/s$$
Now, we can plug these values into the de Broglie wavelength equation:
$$\lambda = \frac{6.626 \times 10^{-34} Js}{(0.0124 kg)(53.6448 m/s)} = 1.04 \times 10^{-34} m$$
Finally, convert the wavelength to centimeters:
$$1.04 \times 10^{-34} m(\frac{100 cm}{1 m}) = \boxed{1.04 \times 10^{-32}\ cm}$$